Description of fast matrix multiplication algorithm: ⟨10×21×21:2633⟩

Algorithm type

3 X^{6} Y^{4} Z^{4} + 30 X^{4} Y^{6} Z^{4} + 3 X^{2} Y^{2} Z^{10} + 16 X^{5} Y^{2} Z^{5} + 174 X^{4} Y^{4} Z^{4} + 9 X^{2} Y^{2} Z^{8} + 16 X^{5} Y Z^{5} + 10 X^{6} Y^{2} Z^{2} + 3 X^{4} Y^{4} Z^{2} + 8 X^{4} Y Z^{5} + 84 X^{2} Y^{6} Z^{2} + 21 X^{2} Y^{4} Z^{4} + 3 X^{2} Y^{2} Z^{6} + 6 X^{3} Y^{4} Z^{2} + X^{6} Y Z + 52 X^{4} Y^{2} Z^{2} + 423 X^{2} Y^{4} Z^{2} + 42 X^{2} Y^{2} Z^{4} + 48 X Y^{6} Z + 6 X Y^{2} Z^{5} + X^{3} Y^{3} Z + 11 X^{3} Y^{2} Z^{2} + 6 X^{2} Y^{4} Z + 60 X^{2} Y^{3} Z^{2} + 42 X Y^{4} Z^{2} + 18 X Y^{2} Z^{4} + 6 X Y Z^{5} + 4 X^{4} Y Z + 18 X^{3} Y^{2} Z + 4 X^{3} Y Z^{2} + X^{2} Y^{3} Z + 415 X^{2} Y^{2} Z^{2} + 150 X Y^{4} Z + 6 X Y^{2} Z^{3} + 18 X Y Z^{4} + 27 X^{3} Y Z + 102 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 48 X Y^{3} Z + 126 X Y^{2} Z^{2} + 10 X Y Z^{3} + 104 X^{2} Y Z + 276 X Y^{2} Z + 86 X Y Z^{2} + 130 X Y Z

Algorithm definition

The algorithm ⟨10×21×21:2633⟩ is serendipitous tensor product (⟨5×7×7:176⟩ - 8) ⊗ ⟨2×3×3:15⟩ +⟨8×3×3:55⟩ +2⟨4×3×3:29⟩.

Algorithm description

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.

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